4. A survey of 40 home prices in a metropolitan area has the following results. Price Less than $200,000 Equal to $200,000 More than $200,000 Number of homes 13 1 27 1. Test the hypothesis that the median price in the metropolitan is $200,000 2. Test the hypothesis that the median price in the metropolitan is more than $200,000 a = 0.05 in both cases. Include hypothesis formulation, use the binomial approach, and explain your calculations in detail. Include p values in both cases.

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## Analysis of Home Prices and Market Returns

### Home Price Survey in a Metropolitan Area

A study of 40 home prices in a metropolitan area yielded the following results:

| Price               | Less than $200,000 | Equal to $200,000 | More than $200,000 |
|---------------------|--------------------|-------------------|--------------------|
| Number of homes     | 13                 | 1                 | 27                 |

### Hypothesis Testing

1. **Hypothesis 1:**
   - Test if the median price in the metropolitan area is $200,000.

2. **Hypothesis 2:**
   - Test if the median price in the metropolitan area is more than $200,000.

Both tests use a significance level of α = 0.05. Formulate your hypotheses, apply the binomial approach, and detail your calculations, including p-values for both hypotheses.

### Regression Analysis on Market Returns

A proposed relationship between annual security return and market return can be defined by the regression model:

\[ y = mx + b + \varepsilon \]

- **y**: Annual return of the security
- **x**: Annual return of the market
- **b**: Intercept
- **ε**: Normally distributed noise

**Return** is calculated as:
\[ \text{Return} = \text{value at end of the year} + \text{received dividends during the year} - \text{value at the beginning of the year} \]

### Model Testing Approach

1. Retrieve annual data for a security of your choice and a financial index like the S&P 500 as the market indicator.
2. Use the past 20 years as your timeframe for analysis.
3. Conduct a regression analysis that includes hypothesis testing.
4. Report findings, include conclusions, significance levels, and present the final regression model.
5. Provide a scatterplot with the regression line, analyze residuals, and check their normality.

Consider if the model is valid. Determine whether there is a positive or adverse influence and specify if your regression model shows outperformance or underperformance relative to the market. Provide a detailed explanation of your work.
Transcribed Image Text:## Analysis of Home Prices and Market Returns ### Home Price Survey in a Metropolitan Area A study of 40 home prices in a metropolitan area yielded the following results: | Price | Less than $200,000 | Equal to $200,000 | More than $200,000 | |---------------------|--------------------|-------------------|--------------------| | Number of homes | 13 | 1 | 27 | ### Hypothesis Testing 1. **Hypothesis 1:** - Test if the median price in the metropolitan area is $200,000. 2. **Hypothesis 2:** - Test if the median price in the metropolitan area is more than $200,000. Both tests use a significance level of α = 0.05. Formulate your hypotheses, apply the binomial approach, and detail your calculations, including p-values for both hypotheses. ### Regression Analysis on Market Returns A proposed relationship between annual security return and market return can be defined by the regression model: \[ y = mx + b + \varepsilon \] - **y**: Annual return of the security - **x**: Annual return of the market - **b**: Intercept - **ε**: Normally distributed noise **Return** is calculated as: \[ \text{Return} = \text{value at end of the year} + \text{received dividends during the year} - \text{value at the beginning of the year} \] ### Model Testing Approach 1. Retrieve annual data for a security of your choice and a financial index like the S&P 500 as the market indicator. 2. Use the past 20 years as your timeframe for analysis. 3. Conduct a regression analysis that includes hypothesis testing. 4. Report findings, include conclusions, significance levels, and present the final regression model. 5. Provide a scatterplot with the regression line, analyze residuals, and check their normality. Consider if the model is valid. Determine whether there is a positive or adverse influence and specify if your regression model shows outperformance or underperformance relative to the market. Provide a detailed explanation of your work.
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